Kinetics: the facts
RATE OF REACTION
is the change in concentration of reactant or product in a given
time
for the general reaction:
A + B → C
the rate is:
-d[A]/dt or –d[B]/dt or +d[C]/dt
RATE LAW OR KINETICS OF A REACTION
is the equation relating the rate of reaction at any time to the
concentration of reactants at that time
e.g. rate is proportional to [A]×[B]2 or rate ∝ [A][B]2
So rate = k[A][B]2 where k is the constant of proportionality or
rate constant for this reaction
This leads to the concept of order.
1
Kinetics: the facts
ORDER
is the number of concentration factors in the rate equation.
In the example above the order with respect to A is 1 and with
respect to B is 2; the overall order is 1 + 2 = 3.
The order of a reaction can only be found by experiment and
cannot be worked out from the equation of the reaction.
Common orders
zero order: rate is unchanged with concentration term:
rate ∝ [A]0
first order: rate is directly proportional to one concentration term:
rate ∝ [A]1
second order: rate is proportional to two concentration terms:
rate ∝ [A]1[B]1 or rate ∝ [A]2
2
Kinetics: the facts
EXPERIMENTS TO FIND ORDER:
discontinuous
many separate experiments with
different starting concentrations
continuous
one experiment
one reading per experiment
many readings as
experiment goes on
e.g. clock reactions;
thiosulphate and acid
e.g. gas syringes;
sampling experiments
3
Kinetics: the facts
FACTORS THAT AFFECT THE RATE OF REACTION
Reaction rate is affected by :
● the concentration of the reactants (and pressure in gas phase
reactions)
● the particle size in heterogeneous reactions (those involving solids
with gases or liquids)
● the temperature of the reacting system – typically the rate
doubles for every 10oC rise in temperature.
(some reactions are affected by light energy instead of heat)
● the addition of a suitable catalyst
RATE DETERMINING STEPS
In a multi-step reaction, the slowest step controls the rate.
CHAIN REACTIONS
are reactions in which each step produces the reactant for the next
4
step
Kinetics: the facts
DETERMINING ORDERS AND RATE CONSTANTS
For discontinuous experiments: inspect the data to see how
changing concentration affects the rate (see example on p.40).
Once order is found, write a rate equation then substitute one set
of concentrations in to find the rate constant.
For continuous experiments
either: 1. Plot the reactant concentration against time
2. Is it a straight line? If so then the order is zero.
3. If not order is first or second, measure and tabulate half
lives.
4. Are they constant? If so , then the order is first
and rate constant is k = loge2/half life
5. If not, work out the initial concentration c0
times the half life for several values of half life.
6. Are they constant? If so then the order is second.
5
Kinetics: the facts
or: 1. Plot the reactant concentration against time.
2. Is it a straight line? If so then the order is zero.
3. If not, plot ln [reactant] against time.
4.Is it a straight line? If so the order is first and
the gradient = the rate constant k.
5. If not, plot the reciprocal of [reactant] against time.
6. Is it a straight line? If so the order is second and
the gradient = the rate constant k.
6
Kinetics: the facts
Words
Words and Expressions
kinetics
rate of reaction
rate equation; rate constant
reaction order; the order with respect to A; zero order; first
order; second order; overall order;
overall reaction; elementary reaction; rate determining step
(rds)
chain reaction; heterogeneous reaction; homogeneous reaction
7
Kinetics: the theory
THE COLLISION THEORY
This states that to react
● particles must collide
● with enough energy to break existing bonds
● and with the correct orientation to bring reactive sites close
together
RELATING THE THEORY TO THE FACTORS AFFECTING
RATE
Changes in concentration (or
Surface area changes in
pressure for a gas ) change
heterogeneous reactions change
the number of particles in a
the number of collisions
unit volume and hence the
between the fluid phase (liquid
number of collisions per unit
or gas) and the solid surface.
time in that volume. If the
Once again, if the number of
number of collisions changes
collisions changes then the rate
8
the rate will change.
will also change.
Kinetics: the theory
Changes in temperature change the kinetic energy of the particles
and hence the number of successful collisions with enough energy
to break existing bonds and make product particles. The minimum
energy needed for a successful collision is called the activation
energy.
Increasing the temperature of the system:
1. increases the range of kinetic energies;
2. increases the average kinetic energy;
3. increases the population of particles with more than the
activation energy (shown by the shaded areas under the graph).
9
Kinetics: the theory
Addition of a catalyst can decrease the required activation
energy so that a greater population of particles will collide
successfully.
A catalyst increases the rate without being used up. It does this
by providing a reaction pathway with a lower activation energy
through:
10
Kinetics: the theory
1. making more collisions have favorable orientation;
2. locally increasing concentrations on its surfaces;
3. providing a series of simple steps rather than one high
energy one;
4. providing a better attacking group which is regenerated
later;
5. increasing the reactivity of the reactive site.
11
Kinetics: the theory
Relating the theory to the rate equation
Rate = k[A]x[B]y
k = Ae-EA/RT
concentration changes
change rate
k is temperature dependent
and k depends on the activation energy
and so is affected by adding a catalyst
12
Kinetics: the theory
Rate determining steps
Like roadworks on a motorway, the slowest step in a multistep
reaction controls the overall rate.
e.g.
O
H+ slowly
fast reaction
CH3CCH3
active enol form with I
2
CHI3
so rate depends on [propanone] not [iodine]
reaction is 1st order w.r.t. propanone, zero w.r.t. iodine
13
Kinetics: the theory
Words
Words and Expressions
collision: collide
activation energy; pre-exponential factor
population
propanone = acetone
enol
14
Catalysis
Catalysis: changing the rate of reactions by adding a
substance which does not get used up
HETEROGENEOUS CATALYSIS
e.g. H2 + I2
2HI
Uncatalyzed
15
Catalysis
Catalyzed
Other important examples:
V2O5 in the Contact process
Iron in Haber process
Platinum in the oxidation of ammonia and in car exhaust systems
16
Catalysis
HOMOGENEOUS CATALYSIS
Here the catalyst and the reactants are in the same phase.
The catalyst:
●might provide a more reactive attacking species
e.g. CN- in the carbonyl reaction with hydrogen cyanide or the
hydroxide ion in the hydrolysis of esters
better nucleophile and more reactive than
better nucleophile and more reactive than water
might enhance the reactive site
e.g. addition of acid in the reaction between ethanol and bromide
ions
●
17
Catalysis
might be able to react with both reactants through having a
range of reactive oxidation states
e.g. the reaction between peroxydisulphate (VI) and iodide is
catalyzed by both iron (II) and iron (III)
●
过氧二硫酸根
连二亚硫酸 dithionous acid; 连二亚硫酸盐 dithionite S2O42Na2S2O4, 保险品
18
Catalysis
Enzymes
Many complex protein molecules have reactive sites that allow
reactants to be absorbed onto the surface of the protein because of
the way the molecular chains are folded. This lowers the activation
energy of bond breaking. Enzymes are usually very specific
catalysts, i.e. each enzyme only catalyses one particular reaction.
2H2O2 → 2H2O + O2
Activation energy in kJ mol-1
75.3
with platinum
48.9
with enzyme catalase（过氧化氢酶） 23
催化剂
Ea/kJ.mol-1
k催化/k非催化
（T=300 K）
无
75
I－
~59
Pt
~50
酶
~25
1
611
22500
5×108
19
Catalysis
Autocatalysis
In some reactions one of the products catalyses the reaction.
This means that once some of the reactants have changed into
products, the reaction will speed up as the catalyst is made.
This is called autocatalysis.
e.g. the reaction between ethanedioate ions and manganate (VII)
ions results in the manganese being reduced to manganese (II)
ions. These manganese (II) ions catalyse the original reaction.
20
Catalysis
Words
Words and Expressions
catalysis; catalyst; catalyze
heterogeneous; homogeneous;
heterogeneous catalysis; homogeneous catalysis
reactive sites; active sites
support; carrier
carbonyl
hydrolysis
nucleophile: nucleophilic; electrophile: electrophilic;
hydrophilic
car exhaust
enzyme
autocatalysis
21
Chemical equilibrium
Chemical equilibrium:
the study of reversible reactions
REACTIONS WHICH GO TO COMPLETION
Many reactions continue until one of the reactants runs out and
then the reaction stops.
e.g. a fire burns until the fuel runs out
marble chips react with acid until either the acid or the marble
is used up
These are examples of reactions which go to completion as the
graph of concentration against time shows.
22
Chemical equilibrium
REVERSIBLE REACTIONS
Reversible reactions make products which themselves react to give
back the reactants. These reactions never stop because once some
product is made it can regenerate the reactants from which it
came.
e.g. acid reacts with alcohol to make ester and water, but ester reacts
with water to make acid and alcohol
To show a system like this the equilibrium sign
is used
acid + alcohol
ester + water
Look at the way
concentration and
rate changed with
time here
23
Chemical equilibrium
After time t, products are being made at exactly the same rate
as they are reacting to make reactants. Because the two
opposite rates are exactly equal there is no external change and
the system is said to be in dynamic equilibrium.
24
Chemical equilibrium
RECOGNISING EQUILIBRIUM SYSTEMS
1.They can be approached from either end.
e.g. chromate ions can be changed into dichromate ions by
adding acid
and dichromate ions can be turned into chromate ions by
adding hydroxide ions, which remove the hydroxonium ions.
2. if the temperature is changed an equilibrium system changes,
but if the original temperature is restored, the system will go
back to its original state.
25
Chemical equilibrium
PROVING THE DYNAMIC NATURE OF AN
EQUILIBRIUM SYSTEM
This is done using radioactive tracers:
1. Set up an equilibrium system and allow it to reach equilibrium
2. By sampling and measuring, find the exact composition of the
whole system
3. Now set up an identical system by adding the exact amount
you have just measured, but with one component made of a
radioactive isotope, say one of the reactants
4. Leave the system for a time and then sample again and show
that there are radioactive products, thus proving that even at
equilibrium matter is being converted either way
26
Chemical equilibrium
Words
Words and Expressions
reversible; irreversible
marble
regenerate; regenerable
chromate; dichromate; chromium
restore
dynamic; dynamic equilibrium
radioactive isotope; radioactive tracer
27
The equilibrium law
The equilibrium law:
relates the concentrations of reactants and products
THE EQUILIBRIUM LAW
The equilibrium law states that for any system in equilibrium,
there is a numerical relationship between the concentrations of the
products, raised to the power of their stoichiometric numbers, and
the concentrations of the reactants, raised to the power of their
stoichiometric numbers. This relationship is called the equilibrium
constant, Kc (when trying to explain this in an answer you must
give an example like this )
e.g. for the system
N2 + 3H2
2NH3
The equilibrium law states that:
square brackets, [ ],
mean concentration
of whatever is inside
them.
28
The equilibrium law
THE EQUILIBRIUM CONSTANT, Kc, FOR HOMOGENEOUS
LIQUID SYSTEMS
Many equilibrium systems are made up of ions in solution. They
are all in the same liquid phase. Here Kc is written in terms of
concentration. For example:
29
The equilibrium law
THE EQUILIBRIUM CONSTANT, Kp, FOR
HOMOGENEOUS GASEOUS SYSTEMS
For gases it is usually more convenient to measure the pressure of
the gas than its concentration. In a mixture of gases the gas is
causing only part of the pressure, so the idea of partial pressure
is used.
The partial pressure of a gas in a mixture is the pressure that
the gas would exert if it alone occupied the space containing the
mixture.
30
The equilibrium law
The pressure caused by a gas is proportional to the number of
particle of the gas so we can write:
which can be rearranged to give pg = ng/NT × PT
ng/NT is the mole fraction of the gas
So the partial pressure of a gas equals the mole fraction of that gas
multiplied by the total pressure.
Using partial pressures, a form of the equilibrium law can be
written in terms of a different equilibrium constant Kp. For
example:
31
The equilibrium law
THE EQUILIBRIUM CONSTANT FOR HETEROGENEOUS
SYSTEMS
Many systems contain more than one phase and so are
heterogeneous. If one of the phases is a pure solid or liquid, then
although the amount of the solid or liquid may change, its
concentration will not. In these cases it is usual to write an
equilibrium law expression that does not contain the pure solid or
liquid phase’s concentration (which is actually included in the
modified equilibrium constant). These examples show this point:
32
The equilibrium law
Words
Words
equilibrium constant
power: the concentration raised to the power of the
stoichiometric number
six power of 10 (106)
bracket: square bracket; parenthesis
partial pressure
33
Chromatography and the partition law
The partition (or distribution ) law states that when a solute is
added to two phases in contact with each other, the ratio of the
concentration of the solute in the two phases is constant whatever
the amount of solute or each phase
This applies to solid solutes like iodine added to water/organic
mixtures, to oxygen distributed between the air and water, and to
solutes distributed between stationary and moving phases in
chromatography.
34
Chromatography and the partition law
Chromatography is the process of separating a solution containing
many solutes, which are often present in very small amounts, by
placing the solution on some absorbent medium and passing yet
another solute across the medium.
Each solute in the original mixture will distribute itself between
the solution on the absorbent, stationary medium and the second
moving solvent in a unique way. The result is that some solutes will
travel across the absorbent medium faster than others, leaving the
individual solutes separated and spread.
GLC, TLC, etc. are initials for different types of chromatography.
35
Chromatography and the partition law
GLC stands for Gas Liquid Chromatography in which small
samples of a liquid mixture are injected into a stream of carrier gas
passing over some surface active solid material (aluminum oxide,
activated charcoal, etc.) packed into a long thin tube. As it passes
along the tube the mixture is separated. The end of the tube may
lead straight into a mass spectrometer or some other detection
device such as flame photometer.
36
Chromatography and the partition law
TLC stands for Thin Layer Chromatography in which small
samples (drops) are placed on some absorbent material spread
thinly on a carrier surface which may be paper or glass. The paper
or glass plate is then placed in a shallow dish of a special solvent
which flows over the surface separating the original sample.
Each component in the original sample can then be recognized by
measuring the distance it has travelled compared to the distance
the solvent has travelled. This is known as the Rf value.
37
Chromatography and the partition law
Words
Words and Expressions
chromatography; chromatograph
gas chromatography (GC); liquid chromatography (LC);
high performance liquid chromatography (HPLC);
thin layer chromatography (TLC)
partition n, v; distribution: distribute
stationary; moving; stationary phase; moving phase
absorbent; absorb; absorption;
adsorbent; adsorb; adsorption
spread; disperse
carrier; carrier gas
column
detector; detection device
recorder
38
Buffer solution
A weak acid like this
exists mainly as
molecules. These
molecules can provide
more hydroxonium ions
if the existing ones are
removed by adding a
base.
Ethanoic acid
This salt contains
ethanoate ions,
the conjugate base
of ethanoic acid. If
acid is added they
can react with it.
Sodium ethanoate
If the two are
added together a
buffer solution
is made.
Buffer solution
39
Buffer solution
HOW BUFFERS WORK
We have seen that a buffer contains particles which can
react with either any acid or any base which is added.
Addition of a base
Any base that is added reacts with the
hydroxonium ions, H3O+, and uses them
up. This means that there is no back
reaction in the equilibrium, but the
forward reaction goes on with more
ethanoic acid molecules protonating
water and replacing most of the
hydroxonium ions that were removed by
the base. so the pH hardly changes at all.
Addition of acid
Adding acid, that is more
hydroxonium ions, H3O+,
increases the rate of the back
reaction as ethanoate ions collide
more often with acid ions until
most of the extra ones are
removed. Once again the pH
hardly changes.
40
Buffer solution
USES OF BUFFERS
Buffers are vital in almost all biological systems where a change
in pH can have a great effect on the functioning of a cell. To
prevent this, all injections and eye drops, for example, are
buffered.
Buffers are also important in industry. Both in the dyeing and
electroplating the pH of the process is essential to its success.
41
Buffer solution
BUFFER CALCULATIONS
For any weak acid:
HA + H2O → H3O+ + Aapplying the equilibrium law:
Ka = [H3O+] ×[A-]/[HA]
or rearranging the equation:
Ka/[H3O+] = [A-]/[HA]
The ratio of concentration of conjugate base to acid controls the
ratio of Ka to [H3O+]. Dilution does not affect the value of this
ratio－both
concentrations are changed equally — so the pH of a buffer is
42
not affected by dilution.
Buffer solution
Words
Words and Expressions
buffer; buffer solution; acidic buffers; basic buffers
hydroxonium ion (H3O+)
ethanoic acid = acetic acid; ethanoate = acetate
spare
forward reaction; back reaction
vital; essential; crucial; key; important
injection; eye drop
dye
electroplate
43
Hydration and hydrolysis
Hydration and hydrolysis: reactions with water
HYDRATION
When any substance is dissolved in water, the particles in it
become surrounded by water molecules. This process of
surrounding the particle with water is called hydration and the
ions formed are called aquo-ions. The equations below
represent these changes for various substances.
e.g.
sodium chloride NaCl(s) + H2O(l) → Na+(aq) + Cl－(aq)
carbon dioxide
CO2(g) + H2O(l) → CO2(aq)
ammonia
NH3(g) + H2O(l) → NH3(aq)
aluminium chloride AlCl3(s) + H2O(l) → Al3+(aq) + 3Cl－(aq)
sodium carbonate
Na2CO3(s) + H2O(l) → 2Na+(aq) +CO32-(aq)
44
Hydration and hydrolysis
Complex ions
The water molecules around ions, for example a sodium or
chloride ion, are fairly weakly attracted and so are constantly
changing as other water molecules replace those nearest the ion.
However, some ions are sufficiently small and highly charged to
attract the water molecules (or other particles in solution) so
strongly that they become firmly joined to the ion, at least for a
time. The particle formed is called a complex ion and the water or
other surrounding particles are called ligands.
A modified equilibrium law expression can be written for this
process and the equilibrium constant is called the stability
constant, Kstab.
45
Hydration and hydrolysis
HYDROLYSIS
Once the particles are surrounded by water, they may react with it.
The reaction of particles with the water is called hydrolysis.
Hydrolysis reactions always lead to a change in pH of the solution
because the relative number of hydroxonium or hydroxide ions is
changed.
Covalent substances
(i) with a positive reactive site react with water making it acidic
(ii) with a prominent lone pair react with water making it alkaline
46
Hydration and hydrolysis
Ionic substances
(i) with small, highly charged cations react making the water
acidic
Nearly all transition metal cations are hydrolyzed by water
making an acidic solution. The reason for this is that the d
electrons do not shield the nucleus well so producing an ion with
high polarizing power.
(ii) with anions which are the conjugate bases of weak acids react
making the water alkaline
CO32-(aq) + H2O(l) → HCO3－(aq) + OH－(aq)
47
Hydration and hydrolysis
Words
Words and Expressions
hydration
hydrolysis; hydrolyze
aquo-ions; aqueous (aqueous solution)
complex ions
48
Indicators
Indicators are substances which change color as the pH
changes
An indicator is a weak acid whose conjugate base is a different
color.
HInd → H3O+ + Indcolor A
In acid there will be a
lot of H3O+ and so the
equilibrium will lie to
the left. The color seen
will be color A.
color B
In alkaline conditions, all the
H3O+ ions will be used up and
the equilibrium will move to the
right. The color seen will be color
B.
49
Indicators
When there are equal amounts of the two colours, [HInd] will
equal [Ind-] and the color will be mixture of A and B. This
happens when pH = pKInd as shown below.
KInd = [H3O+] × [Ind-]/[HInd]
when [Ind-]/[HInd] = 1
so KInd = [H3O+] and pKInd = pH
The sudden change in color seen in a titration is called the endpoint. Some people are color blind, but most people can detect a
change in color when the ratio of A to B is 1:10 or 10:1. This
means that most indicators have a useful pH range of about 2 pH
units, about one either side of the pKind value as the table shows.
The equivalence point of the titration, when amounts of acid and
base exactly balance, and the end point will be very close to each
other if the correct indicator has been chosen.
50
Indicators
Indicator
Methyl orange
Bromophenol blue
Methyl red
Bromothymol blue
Phenolphthalein
pKind
3.7
4.0
5.1
7.0
9.3
Useful pH range
3.1-4.4
3.0-4.6
4.2-6.3
6.0-7.6
8.3-10.0
Color change
red to yellow
yellow to blue
red to yellow
yellow to blue
colorless to red
51
Indicators
INDICATOR STRUCTURE
Indicators are quite complicated molecules whose electronic
structure changes as they are protonated or deprotonated. This
change in electronic structure results in a change in electronic
energy levels and so a change in color when light falls on to the
molecules and moves electrons between the energy levels.
52
Indicators
TITRATIONS WITHOUT INDICATORS
If one of the reactants is colored, an indicator is not necessary. In
particular, redox titrations such as those involving the reduction of
manganate (VII) ions or iodine can be done without an indicator.
For manganate (VII) titrations the color change is between purple
and colorless. Dilute sulphuric acid is always added because MnO4is a better oxidizing agent in acid conditions and the end point
occurs when the color changes from purple to colorless or from
colorless to a faint pink.
Iodine which is brown in solution is titrated against thiosulphate
solution. Here the end point occurs when the solution goes from
pale yellow to colorless. This change can be make more obvious by
adding some starch solution once the iodine has reached a straw
color. The starch forms a blue compound with the iodine which
disappears as the iodine is used up.
53
Indicators
54
Indicators
Words
Words and Expressions
indicator
titration; titrate
end-point
color blind
equivalence point
deprotonate; protonate
pale yellow; pale blue; dark blue; faint pink
thiosulphate
starch solution
titration curves
55